Kinetic Theory

JEE Main level, single correct, medium

48 of 168

Question 48 of 168

The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are vH,vO{v}_{H},{v}_{O} and vC{v}_{C} respectively, then:

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Answer: (C) vH>vO>vC{v}_{H}\gt {v}_{O}\gt {v}_{C}

The formula of root-mean-square speed in terms of absolute temperature and molecular mass of the gas is, vRMS=3RTM⇒vRMS∝1M{v}_{RMS}=\sqrt{\dfrac{3RT}{M}} \Rightarrow {v}_{RMS}\propto \dfrac{1}{\sqrt{M}}, here we know that, MH2<MO2<MCO2{M}_{{H}_{2}}\lt {M}_{{O}_{2}}\lt {M}_{{CO}_{2}}⇒vH>vO>vC\Rightarrow {v}_{H}\gt {v}_{O}\gt {v}_{C}.

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